{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# GMM\n",
    "代码来自sklearn文档"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "E:\\anaconda3\\lib\\site-packages\\sklearn\\utils\\deprecation.py:144: FutureWarning: The sklearn.datasets.samples_generator module is  deprecated in version 0.22 and will be removed in version 0.24. The corresponding classes / functions should instead be imported from sklearn.datasets. Anything that cannot be imported from sklearn.datasets is now part of the private API.\n",
      "  warnings.warn(message, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x1e0a58e1588>"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set()\n",
    "import numpy as np\n",
    "\n",
    "#产生实验数据\n",
    "from sklearn.datasets.samples_generator import make_blobs\n",
    "X, y_true = make_blobs(n_samples=400, centers=4,\n",
    "                       cluster_std=0.60, random_state=0)\n",
    "X = X[:, ::-1] #交换列是为了方便画图\n",
    "\n",
    "from sklearn.mixture import GaussianMixture\n",
    "gmm = GaussianMixture(n_components=4).fit(X)\n",
    "labels = gmm.predict(X)\n",
    "plt.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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kPKTjkizIpcexpDkzUDiRilLeQ2totOMVT1+PEsVkLWCq3mWqHjBV6zJZ7zJRC2h1YxKpe8aXLUUQJYxPdUxLu8GwAPsTn/jEJ9bzAN1utOyUkyyKRZ9Op3/k1UbHdSw0uqeBRSBwXQuNIJyXU3Ydm9FLdrHv7icAsSbt7M9+8wFEzqN9uIZf8PGKOQDiRDH+1Mv84+98me/8wW28/ODzlLcOkRsqk/OdJaVWA9ONkGRB+kbrNIIPY0k3SogThW1bOAtKB/M5j2BBo49Umm4oyeWc41Jq+GqwWT/jS3EyXjOs7rqFEBQK/WteYKpEXhU0molaQDforQRxfIeXD9R7HlMaqo0urzzwHK1D09z/uW+tiUuTk3fRiea8Gy7jR37pZl645ym++Zt/QxLFqQILcDyXt3/s/bzmrRdTzi+ezw4iyfS8cWhLIQTkfIdy3sOxUyEeGixSXWSSvG0LxgYK6VSbTcZm/owvxsl4zWCqRDY0AsFwxcdZ4NhXKniUFjTaWAIGyjl2vvZstl++e81c/pJujIwTnr79IR78yj3c8d9uTceXzaqyTm1gv/vpW2m1IsJ48eh+NbasWqf2rlP1Lp0gWXZRU0rN4Vpq1WrWIQ0nO0awXyUcy2K44veJUKngzrn6HXmuoFhwiZrBmhs0JUHMv/z1PxMH2V/XwlZA7VCVWivKDOwFHNU3KKk0tVbIVD2gHcRLplxmx5s1TsKv0gbDfIxgv4oUcg6VBfXZs65+1oK8bc612XbO9nUZehA0u4vuVyuFm/OQUi1aJ30st5AoTie019vZN4RZlE4d/+rtyAxFMJy0GMF+FdEaBjIG+DqWxUDR66uqqAzkufi9b1yXc6lsHep7TFiCLWfvpDBTqRKGklo3YCqpE6p0kVDPPO9Y0Bpa3ZjpekC8RCmg1lBrBlSbpsHGcHKyosaZD37wg0xPT+M46dN/4zd+g0suWeMa4ZMUIQQjAzkOTXV6Hs/5DkWlac3z/BAI3vjhG5h44QAH7n32aA4GaBYmjlUsqR+c6nt6rpLnlk/+HwBorbkjeYD7p58k3YtmT/F83jvwRtw1yqtHiWS63qVSzJ5CT3r21FshUmlGKv6KSwUNhs3AsoKttWbv3r1897vfnRNsw9piW4KRwRzRfCHVUM65JInqaR9/+H/dxYH7jkKsAcu1yY9UaB+c7tumMhYOZaIobxmgm2huDx/gfvUEMUdK977ffhKpFe8tX4sQHFX5ptKK56L9HJZ1dlijDKsKtVZInCjKRW9ROW51IrTWjA7kjGgbThqWVeAXXngBgJ/+6Z+mVqvx4z/+4/zkT/7kup/YyUbesym4DrVqp0f4BooeiVQkieKFu5/krj/+el+EvFJUlBBUWyt+vpaKx779MGdffzH3dnrFGiBG8sPO07yr8gYsSyBX2dk4qWr8VfwtojhGa41Cc451Kjc7b6bVjYkTxWDGIIhZ2t10sXJ0IIdJbBtOBpYV7EajwZ49e/jYxz5GHMf81E/9FLt27eLqq9dvxNXJiNYwUskxWXBpto80kVhCMFT2maoH3PXHtx21WM8iF6kGyXxuLKmN1+iIkMUO7AibmmySs0pIufJWdqUVfxV/iyadnl0/o17mHvkol9rncCBo4cQ2A0Wf03OjWKI/9dLqxiCESY8YTgqWFezLLruMyy67bO739773vdx5550rFuzFCsBXwthY+ahfu1E56/QRDk62+uqe83mPxqHqcT0X27U5/dJdjOTKUM8WwwTJruEtyMCi0V75zeD56BWiqN8HO0Fyl3yYu+TDKBQ6ASu0yFkuH97xNl4/cF7m/qSw2TJc2HBdkSfjZ/xkvGZYm+teVrDvv/9+4jhmz550CrfWelW5bNPpuHLGxspUp9s4aKYaQa+XhoDSSIXGeO34nIyA4dO3MHz2TtqNiNd553Nv9ATJvLSIg81F9pnELYVUknY7WLH3yISsL/plQdJ7s1IoOirkj/bfRi70ON3rn4VZrUG93mGkklvxJb7anKyf8ZPtmuE4djo2m00+9alPEYYhrVaLW2+9leuvv351Z2tYFY5lMTKY663F1nDdv7ke2zt+C7+NQ1W+8V/+mul9E9zgv45LxNk42Hi42NhcaJ3J2609dIIEx7JwnZW3j++wRpGszg0wJuFrtfsX3d7sREw3V9YibzBsRJb913/dddfx8MMP8+53vxulFB/4wAd6UiSG9SHv2QyVfaYbwdwi5FXvvZrGeI1//vPvorVCSYXjuWlL+VqjoVtr89ydj7H3h0/zvj/8OW7efTVvaF5C5IWUKZAT6ZCFVifGc20KOYdghZNyBkWZC6xdPKn29kTty3EgnuJLE9/DchWX5M7kXP+Unu7P2bTMcCV3zPl+g+FEw5g/nUBkXXO1FdJo9eaG240uzz26D79SZPLFQ3zrt/52biTYuiBg1+vP4z2/9yHqrQjbFrgLZoj5ns1g2WOiFiBX6CqotOIH8nEeUE/S0SFjYohDemrOm3uRUwFSLfaEyzneDn525EbsBQuSlaJ3wou2+YyfPKxVSsQUVp/gDJY84kT1OPsVK3ku3HMOU/WA0lgFx3PXV7A1vPLwi8SxZKDoMl7t9nVihpEkiCQ516a9QsG2hMUe52Le7F1GtxMhhODPk39gnP468XmnMkekY56JXuG+zjO8vti7GNlop/sbKvsntGgbDKvBtKaf4AgEo5Vc/+R1y2Kw7ON4Lrf8t5+hNDaAm/dwZgfZWgLLtSluGeS6X/8Awj626gm34KepGSHIew7dMOkrfW62Y1zXWrGrntZQb0U02zH1VkitFZCo1Xl+RzrhrvbjmdsarZBaMzQl2oZNg4mwNwCWJRgbzDM+1empwvCddLiv3rWND33pVzj4xMsE9Q5bzz+Fbjuk2Y4obR1ECMFbfuOn+M5//oujO77ncPG7rgTS6TSVksf4VAffUz2piHRYgcJ1bKJ4+bx0GEuSROL7MzcZDa5e/UcykAmJ1HP+2rPMtrEjYPAYhhobDCcKRrA3CK5tMTyQY6oWoOYtO+R9B6k0zXbEjotOn3u8OFymFEta7RjQVHaMYDn2UQ319Us5XvsT1wAzw9iVplz0aHdjKkWvJ+UQBgl+zsaKYalYWUDmCLAL5FlMWlUS0XueNhYC0bdAKRCcz+lMN8IZj/Fs0RZCMFj0jqp93mA4UTApkQ1EMecwWPF6Uw4aSjm3b/ABpJaspUL6uOP3b18pYbNLc+pIS3ucKIr59F4fLoikNZAkOp28cBTslqdzutyJo23QYGkLW1uco06nTKHv+RrNk3ofYRKlY8oy2uNnXf5a3dgMQTBsaIxgbyC0hnLe6/PQBigXPHIZDnc5z6aYd3FyHtsvOwtxFM56tutw8NkDPY8liWKo7GdOjZFS9fl5910L9E3cgTRifkv8et4ZXsflyQVcmpxHQed5TrxMlexV9kld4wm1l0RKppthpqeJ1jDVCOiEq/+GYTCcKBjB3oAMFv25yLnn8ZLXN30d0rRJseBy1c+/k9LWoVWLtkok/nC5x6taSo3r2PiuRTeMexb2tCYdMab0kut99oLzqIsmDztP8aj9DHlyvC65mJbo0BZdYrF4fXdMwmMyNSlLEsnUIqKtlGay1iFcxUgzg+FEwuSwNyjDFT+dLD6v3C+dVuMz1QxIFohS3nMYGi3h+C5CiBVXugnbYujMbVR2jNANYtzikeg+ihMGyz7jU93MBUjHskikwl6kQsUSR4Yf/NB5mEedZ2bn/3Ivj/Da5CKet19CieUF1hFHblRJkkbaw2W/79hSaSZrXbYO5TMjfIPhRMZ8YjcoAsHoQA5vQbmfZaW1x47T/6fd//0naR6cWvHCo+XaDJw6yvCZ23n4S//ExIvjJPOqVLROxbVUcGh3k74o27GtJaNs2xLYlsXL+hCPOc8ihUIJhZz5uc95pM9XJAsXh0uss3sei2dEO8vbJE4kE7XuUTV0GQyvJkawNzCWEIwO9keKjmUxVPaxF3QjPn/XEyTBCtvYLcGWC06jdbDKM7fdxxNfvotv/Ic/5d4v3tHztChWlAv+TElf741AKYXvWkumIGxX8w39vcz29DTaFtmNLzNpF0c7nC1O5WzrlL6nxImk2gjJKu0OY8lkPViyq9JgONEwKZENjmtbjA3nObygRtuxLIYHfKbrIXJGsfxSnpWOhrEdm4mn9iNnfEq00sgo4cEv3ck5b74QN+fx+Nfuo35wmtMuO4vdb7mEdpDglay5Dsg0yrYJosUj+jvED2nqTnZzi0jdIdOdpb+j0xK/LWqEETXImepUdogxpA1Z3lNRIpluBAxXciy4f9EJY6YaaWOSwbARMIK9CfBsi5HBPJMLvuY7lsXQgM90PUApzYU3XsETX79/RbXItucQtfqd72SUcPeffpNXHnwBJRUqkbz4/af44Rfu4Mbf/zCBP0jePfKxklKR9x26UULetXvi2UBHPKn3LX0iC0oYAS6PL+RyeUHPw/V2SKngkXOsvpg5SiTVZsBQJddXbdjqRNiWYKhkGmsMJz4mJbJJKPg2QxW/r87YtawZoRJsPXcnK/X6kku47u37wdMkYTyXC0+CmPZ0kwc//y3CQPalGWzLwhZWX410W3dX9wEU6c+D7hOE9Hqn6JmBxd1IZgbrYSyptcLMBEijHVLvRKZG23DCYyLsTYKeaaCRUlFvRj3C5NkWgxWfaq2LQKwob2s5aeOKjFdml6qV5vm7n+Ca//jjdCNJwVsYZds02hFF25k7ekUUUStYVMwirSjRVEWDmJi61cLG5tzoDK7SF1Lx/b6rDMKEhhAMLKhjn22scSxBKe+abkjDCYuJsDcZAyWfUrG/Rtt3bIYG8uy89MwVmSHFQYSVUdO9FFrDYNkjSVRP+/zsNt+3ieYtQLrCYZfYuapjQDpG7AHncf7FeYIX7f3st8dpWm1qVoP7ncf5kvoGrTDOvMx2ENPs9C+8zjbWdE1jjeEExgj2ZkPDUNmnkNGq7rs2N//ae/AKueXFWGmSMF5xk40QgtOvOBul05vGwkEGSml8xyZe4B/iHu2XPLHgZwYpJFXR4LHohUXTI61uRCdI+rYppZmod/rO0WA4UTCCvQlJa7R9Crl+MTzlnJ383//rP3L5e69m2wWnsfu6ixeNuB3fnWts6dm/JeZ+IF2g9Eo5rvl37yRJFL5rY9uiL8pWSlPwHYL4iJA2dTv74HrBz/zHl/mGkAjJi9YrtLrZOW2tU7/sTkb1ipSaiaqp0TacmJgc9iZFIBgdzDFRC3q6IQHGdgzzjv/wbmrNkCSW/OH3nshuptGaq376en74uW+jlUZLhZPzKI5VeOt/uIUnv/4AjUNVdl6yi4tvvorCYDolI4oTBgo+9W6Eb9vzd5fWjEeSRGlsS9BhmRmM80bMeDgo9PIjxTS8Yo3zP72vsiUZ4c1cyqneaI/uK61ptELsSg5vQZNRlKQ12mNDuZ4hDQbDq40R7E1MGmnnmdTddODAPHzHZnggR7Uecva1F/PsPz3aJ9r5gSJBtYVAICxQWlAcLfNjv/chKluG2HnxGZnH1ToVxILnkkjZI3pSago5l2Ynophz0rmQepHRSaL3vyO9sgVQgMAKAdir9/OyOsj7ouvZ5W3rEW2pNLVmlGnL2gljqk3BcNnUaBtOHExKZJNjCRgdzGU6+bkzzTVv+aWbGTptDDfvYdkWbt4jVylw9rUX8+hXf4iME2Qs0UrTOFjlax/7y2WPGycK17GwM1rkLdIZkInUXG6fi0NGPn2RRppFA9756ZP5LfIiTZF8S95LlPSnORIpqTazuyGbnYhm15T7GU4cTIR9EmAJwdhAjvFahyjqVSbHsti+Y5Cf+twv8OK9zzLx3EHKWwY4840X8Ocf+L2+VnYtFdWXJ5h47gBju3csedwoTijmXDoq6enClEqT82zaQcK51ml8jXuO/SKXEdUJMU2jEzBQzPVF0/FMY83wQK63T0dDtRni2jY5b3UVMwbDemAE+yTBsgRbhgocnu4Qxf2iPTJQwN5zHqddccREqVvNXhC0bIvGodqygq01RImiVPSoN8OebTLR5D2HB6MXcLCIl8tLrwFSKZqdGKeQYFkWRXEk3RHGknorYnBBjbZSmql6wNZh4+5nePVZsWD/7ssvtDYAACAASURBVO/+LtVqld/5nd9Zz/MxrCO2EIwN5Tlc7RIvEG17xuWv1goJZ6onBnYMU3tlqm8/MpaM7Nq6omNGsaSUd8j7dl+NswVEIlq8jUdzpNEnK4JeQcXIfL7l3E3NbtKM2wgBo2KQdzpvZKs1DEA3iHEci3LO6TmnWEom6gFbhwpHO0jHYFgTVhQyfP/73+fWW29d73MxHAccy2JsMN83hR3S1Elaw53ex/d8+Ia+0WK253Dq5bsZ3Dmy4mM2OjGDZR97gdpJpdnlbM+sxBDA6WI7r0su5oLkLGy9ICWhl3Dyy0LAPucAdauZWriiGNfTfDH+Om3dnd1l2t6eMUA4jBKmm4GZwG54VVlWsGu1Gp/+9Kf5yEc+cjzOx3AccG2LLRm2rJCK4EDRp1z0OOea1/Ajv/xuCsNlLMfG9hzOf9vl3Pjx96/qeEmikCptqFnImB7mPO+0noVHgcDD5SZvD6/jIt6UXMEb48vxtdtTl71o5L0YGc9NUDwon5n7XWlNvZk9G7LdiWi0zSKk4dVD6GXcgH7hF36B97///Rw8eJB7773XpEQ2EZ0gZny6k2nyD6mTXb0VIZUiaHbxCj52lofpArTW7L3vWZ7958dxcy4Xvv1yzrr4dIYqOcarbcJoYUmG5p7uo9zVeYxAR5ztncINhdcxYg8QRJJGO0Rr+Ir6Dvt4Zc0drC9wz+BfD/xoz2O2LdJvIguuVwgYG8pTKRp3P8PxZ8kc9t/93d+xfft29uzZw1e+8pWjOsDUVOuousbGxspMTCxSn7tJeTWu2bdgohH05bTntttQ7cRIYdHtxsDSAxCUVHzt1/8n+x98gTiIEJbgvr/+Hld+8Dre9Qs34SGotnonwZQrOa6wzufywnlEs+mIDjToIgAlJbVuh5dyB9FrHd1qUDE0mt2+Td1uxHC5X5ibjbVZhDSf8ZOH1Vy3ZQlGRkrZ25Z64W233cbdd9/NzTffzGc+8xnuuOMOfuu3fmv1Z2s4YXHtNKe9cNTYLI5lMVLJruPO4unvPMTLDz5PHKT2p3rGk+TeL9zBwecOpoublX4RjCJJznOwFuQbNFDwHbSz9EDfnhesBgEqITMFEoQJzW6/iVQszbQaw6vDkv8KP//5z8/991e+8hXuvfdefu3Xfm3dT8pwfHFtiy3DBSZqXcIMtzpLpAb/bcei1Yn7PELm89jX7sscQyal4qHbHmDbv9tOwXcpFSStea55WqdCWCy4NNtR3+u35Mr4ibd0K/sqq0ZmX5MgaXZjBoteX3661YlwbIv8gjrsIEqYboSMmGk1huOIKSw1AGnJ35bBPPklIuli3mVkMIe/hNPfYoMPtFTEM0KeSMVg2cdd0AUZhpKc62Tu33MsrhIXLR1BH2W6ZFCXkYlc1Ha10cpehGx1I9ornZFpMKwBKxbsW265xSw4bnKsmTrtLJc/IB16a1kMV3JUil5f+gLgnB95DY7X/3on53LutRcd2ZXSjAzmsOaV+mkN3TBhsNRfAqiB13nnYa9DjOHq9HyjOMkU4NRzJGThUozWMN0IjB2r4bhhImxDD4LUe6RY6PfTnk8x5zIy0B9tX/zOq6hsH+6p33ZyLrv2nMdpl+6ae0zr1Mtk4fSXIEoQlqCSkZ5whcNV9jJR9lJkvU7Afe6jxKTfDLphkjk0OEpkZqpGKm3y2YbjhmlNN/QhEIxUfCwBzfbiX/kdO422u1FCO0iIY4mb93jfH/5fPH7bfTzz3UdwfI+L3vE6zr324r6qCqk05bxLoGB2/VxKTRhL8r5DFKu+iPda5zLuVY8vb7G6kCX0VKHZZ7/Cbnk66LTc0XWsvii/E8bYjqZht8gJj2GnDKRNNdVmaJz9DOuOEWxDJgLB8Mzw3kZrifZxIO855H2HMJZ0ujFC+Fz6nqu59D1Xzz2nWHBTwV6wo0RqhgfyTFc7JDPjwzpBTMGzKRc94kQRzbN9FUKwW5zCU2rfynPWK1iMbNDmQedJGqLJVjXKuZ1djJUKPc95KH6W70zdhxYapRXb3RE+PPw2RpwKzU6E7zkUV1hNYzAcDSYlYlgcDYMln4Fyf3oi67m+YzNUyTE6kGOo4lMpeZSLHsMDOcp5b9Eo17YFIwO5uWMksSZKNJaASkY++xrnstTTYxVt6cvxL+4TPOA8xlPOi3zPfYAvOH/PoaA2t/1FdYCvy+8TEBHqmBjJy/EE/23iK0gt5/LZiclnG9YRI9iGZRko+owM9C4QLsrMVJmc61D0XUo5F3+Z7kit0yqQ2dZ1pTVBnM5c9B1BueD1aO6oNci/cd+NLfoj9qNFCokUqdgqoQiI+Av+gcm4SaIlX47/CblgwrtG09URjwX70n1IxVQjNPlsw7phBNuwIkp5l7Gh9bMYlVJTKXjk/VTcu0Eqjxoo5BzyM5UrSaLphAl+UORD+t3rN8JLpPXZX05u567kYUL6FxwBYp0wkdTnfu+GMXXjN2JYJ4xgG1aE1pBzbbYOL94VeawkUjFcSW8KUqojbepApeARJop6O6TTTQgjiR143BJfnzr5zar7wqG9K2ExcRUwKWrcLR9Z9KUWFtvcoZ7HGq2ITkYDksFwrBjBNqwKx7bYOlxYvFb7GBEChis+QkA4z9+kG0nyrt2XlhmVw/xM/B7e2L2Sy9oXc3nrEmy9xh/rJaJlH5fz/dN6HlNaM10PFjXVMhiOFiPYhlVjidTJbkWLkatEzYwPKxd8oigd4KsUtLsxQggGMuqzhbS42DmL86Nz2BKNzuWi5zgW3Vzi+gTw4+5b6AYy029kqrHMRHiDYZUYwTYcNUMln5HBfF8Vx7GSSM1AycNzLaTSJEqhpEYpjefalAte/4s0lPMOD5Qf7t+2DvlkgeAy61x2WGO0OjFh0l8d0gli6h2TzzasHUawDUeN1lD0HbaOFNY8r62kYrCcQwtNkqi5IFlK3bMIOfd8rbEti2l3+rhMhRHAa6zdc8derFa93gozOycNhqPBCLbhmHFn8trFgrtm0aQGhIaBgsdCc0ApNQNFD29BW7xUx6+gTqN5UR+Y+z1KUvfBhZc/O8TXpLMNa4ERbMOaYAnBaCXH6CKjx44GpTWuY1HJGCKgVCratt0rkWNqaM1qs5fCwsaj12+lHcSESf/Bo0RSb4cIkS6qzld1ky4xrAbTR2tYUwq+Q27EptYOaXXivuh4tSRSM1j0qBfdHl8TrdPJHAMlj2ojHSG2z3qFKau2xN7WlgvsM3p+V0rTaIdp1+a8xy0haHdjpNLEsUyjbQ2dRNPthOQ8G8+18RybZSb2GU5yjGAb1hzLEgyXc+Q9h+lmOOcRcjQopbGstEU+ThTBvPpmpTSek3qOvNye4jvePSRiQb54vv6tVTSr4U3J5eTdfN8+o1jS6sZU8i6aVKyl0hyudQDB6EBurtknlopWJ6bVibEsge/ZFPMuec/GtsQx3+wMmw+TEjGsG3nfYdtwgXLx6HPbjm1hWxZKaUYG+tMtUmoKvsvTuef7WschreY4JziL3d0zsbSFoxwsvQYt7Ro6Yfawhnb3SGpECJhqdIkTRTyT5866cSil6QYJk9UuBybbVFvhkpN9DCcnJsI2rCv2vGi71gqJY7UqrfRcC8e2sEQacY4O5jhc7fYMdpZS0bLa6IyVPS00gdfh6uoeLuicy7RbxVce+/yXeS7/4lFH3W0Cwigh7zo4Tu9OZlMjW4bytIKEeN43jFY3xvfS9MdiSKmpNyPanYTBskch56xfC75hQ2EibMNxIe87bB8pMjacJ+c7K4q4bVuQ8xwcWyAsMbcIOdsJOZ/TxBYc+kXQ1jY79BZKBZeCzrMz2s5oMsJIMpyK4NG0sgOnqm1EOuLO6CG+Hd/LuJru2R7Fkm6Y0F3g563R1NvRigyiEqmYrAUcmu6Y0kADYCJsw3Fm1js7iNIJLuEiQmQJMTcqTACea5MkCik1ed+hXPBptMO5519qn8s98jEkck4KhQYHm3PjM3Fti2LBpdWJeMnbz/3lh9Di6FMO/+B9l1jMpEQU3KueYDsjfMh7B2LmbtIOE7qhwloQFs2mRoaGWBFRpDhc7ZDPuQyWPDzHMvntkxQTYRuOPzNGUluGCmwfLbJlME+l5KULbjmHwbLHlpEC5ZkxZVqDP68xR0rNYMmjkDtSVpcXPh/y3sEuawcCgdCCHWorPxZeTw4fqTS+a1HMuzxSehy5cHFymfPtQZCK9YISvYNM8Y3k+3O/K6lpdbNd/lpBTDfIzoFnnoKGTjdmfKpDrRWaapKTFBNhG141tNbYlqBS8gm7R1q4Z7VovialaZRw7rHU2c9HKkkYpTniYVHhA+7bEFY6ZqzR6i0rlFLjexZtq7O6E81K3yyS0nlYPceP8oa550RxQhjbPTec2Wuvt0N8i1Xlp9OBwBFBpBjOmDxv2NyYv7bhhEFrFv2q7zlWnzhprRmp5PuaZ7QS5D2XcrHfc0RJ8MnwIlkj5leqCAQaaAdJZqdjnCha3eyqkeUIwoTx6Q7tIDbNNycRKxLs//E//gc33ngjN910E5///OfX+5wMhn40FPO9nYWzzTMjA+nsyfnMlvuVih4KTSJV+qM0FyXn4Oilp+AcLUXmD+LVWJZAynQBMktXW92Y6Cjr1OVM2/uEaX0/aVhWsO+9915+8IMf8NWvfpUvf/nLfPGLX+SFF144HudmMPSQ95w+YVZK4zs2wwP9lSNSKRwrtWdtdeP0pxOxu342Z4SnYWsLS4v+HPXRip+Gt9mv73lo1skwCBOSjLT5bGrkaF1QtIZ2J2Z8uk1s5kluepYV7CuvvJIvfOELOI7D1NQUUkoKhcJyLzMY1hzPtXDc/jhVKk3Bdxgs9XqOxFLRaEWU8gvc/TS8tnkp75h6O29pv5GzotOxtIU701TjKe9Ic81Kyv50WpFybfQ6dqlT5z88N3BBaU07jDNfHseSzioWILOIYsX4VJoiMWxehF7hcvNnPvMZPve5z/H2t7+d3/7t354rXTIYjidT9S7VZpi5TQjBdL2b5oWBRiukG6XDBWxbUG2GRHF/FOpY0JEhE1QpW0UqusykNc1e5yViYp5z96IWDkWYh4XF63kNr7cuQVgwOpDDEhaeazFZ69KdaacXQKXkkvPd/n0IwZahPK577KmacsHN7Ao1bHxWLNgA3W6Xj3zkI9x44428733vW9FrpqZaPV1pK2VsrMzERHPVr9vInIzXDKu77lgqDk11Fv1M2bZguhHSDmKqrRA5kx8WAlzHZroR9HQezuI4aft7N0rwHYv5K4HfGLqdut1YcnHw/OQs3hxfAcBAOYdrC1zHohtKaq0jk2dc204n9QDlcp5mszu3rZh3GSj6a+I2mM85MzeOEyuwMp/x5bEswchIKXvbci9+/vnnefLJJwHI5/PccMMNPP3006s4VYNh7fAcu88Hez5SaoYrPvmc3SN8Ws+UApZzmaVwSaIQInUbDCJJIo+8+A2NK/G0h9DZ4udqh51qy9zvYZQuMCZSzU2BnyWWknCRAb2dbjK3AJkoRRAncz+JWl1+uhskHK52V/06w4nNsoK9f/9+PvrRjxJFEVEUcfvtt/Pa1772eJybwdCH1ppSfun2ASXTcr+c1yuWSmmkUgxVskVbSg0ISgWPKJEEcQJoKrLMO6bexiWti/qMoyxtUVQFzpCnzD0WJQqlj1SxLDxWJ5SZVR0aTbsbU++ETNYCqo1w7meyFjDZCOiEM+K9gsA5jCSHq12zGLmJWLZx5pprruGRRx7h3e9+N7Ztc8MNN3DTTTcdj3MzGDLJeQ62LWYEth8NoDVjg3miWPakQNJJ5qloTzeCPutXKRW2LagUPdqdiHYg8X0bVzicG+zmlGgHDxYf4YB/CD3zv1JcoqE6DFnp11glFbFUcy3kvucQJ9G8c5CZLflCCJqdCKk0uQXfIrROvbTrsUQIge9alItemqdeIoUSx4rx6Q6jA/03MMPGY1U57KPB5LBXzsl4zbD66xYCqq2QejO77XuWdhDTjRIOT3d6UhyQlttZtpUt2koRJwmlvEcQKYJIkvNsHNtCofjm0B207BZq1otEpwuPN3avY6cYBdLOzHLeRYjUuGp8ur3g+BY7t1bodsN5j6X5d6VhsOQtm38WQlDIOZRy7lw1ymJYlmC44lPKu6+qD4n5jC/PUjls05pu2HBoDcVcOoFmqWDAtgRawehgvt+SVWkQaU57upmKttKah/bt5ZlDB4G0U/GiU3Zywc5TaYcJrtKMlw7SsTpHxDp9Ikor/jF/O9uSMV6nLuJUuQ1IHQZ9O7WITeT8SF8RRL2lfEqluWutNN0woZjrrybpfR/SFEoQSkoFl7xvL9rmPjtbUipNJWvqvGFDYOp+DBsSz7HI+0vHG/aMSFoCRgby/Y01UqN06snhOBYPvPgCzxw6iFQKqRSJkjy6fz+Pv/IyA0UfpTQHrcMkVsai4YwR1CFngtu8O7nTuu9IM4zWmQul3QW5bKn1nKd3N0xIVvjNVCpFvRUyWQ+I5OL5ba2h1gyptrLLIg0nPkawDRsSraFc9Jb00XBsgW1ZxInGcwTDlXzfc1LR1hRyNs8fHkeq/vTI4/v3I6WkUvQokE8XHhdDgBSKp60XeSk5DKRzKbOiZaU00bxc9vxrmY2eV0OSKKbrAc0lXqc1NFoRE/XgqLsrDa8eRrANG5aca5HzFo+yhRB4XvoRj+K0xG4wYwK7lJp6pzvXRr4QDbTDkDhRnJPsWpG7XoLkSfViun+l8Vwrc/+daJ5/N0dEO+9Oc/bIrZw1/OeMFB5kpcXZWmta7ShN8yxR0tfpxkzWjGhvNEwO27Bh0RoqRY8gSrIX0nTqPzLrOx1GklI+zd/WFnRLFlxvpoIkG99JI2Q/zrGneQV3lX+YblhCu1+RE7yQHGSXvQ20Ju+7ff7YUkqiSOJ7NkKkN5nThu7hTWd9FoTGFjFS/QP1YDf37v8kSi+d154ljCTTSchAycP37Ey97wQJk7WA0cHcqixeDa8eJsI2bGhyvo23RLma56RDfGcJo4RSwevxHVFac6heZ7hU6KvMsC2Ls7ZsxbGPHGNnuIO3T78FRzssNbTmkJji75Lb+Vz0j7wSVSnk7UxZ7M410gh8p82bzvosjh3hWKl1qmMHDOafYdfQV5Z8LxYilaLaCJdMkcyKtom0NwZGsA0bGw0DhcVz2cIS5BZ0G4ZhQrngUil5NLsBX/zne/jmw48x2WjNTXLxHBtbCM4YHeO1Z+zq2++AqnDT9A2c3zkXR2UIt0gHACci4ZCe4k+iW/n9zl/xlPd8374SKYmT1E/k1KH70Rn/LG0r4rTBb67sPZmHJk2RVJdwBOwECZP1o3cMNBw/TErEsOHJ+w6uaxFFGTlbDTnPnlvAC+KYu558nkf2vZK2jytJK+hNUwhguFTkx658LXGi6AbZreQ57XNx5wIu7JzHfv8AzxWeZ9Ku9s+KnHFw7RJxt/UgwrI5R50x/xSJkgTfdcm5MYLs3LNtHX11RxAkVKVmsORn1mx3ujGTwOiAb9IjJzBGsA2bgoGSz+R0NzNGdB0L27YIwpg//fbdVNudvmqQ+WjgcL1JFCcMFPNYxD22pd0o4vFX9vPK9DSObXH2tu3s3roTW9vUKvcTs7hVaozkfvcxzgnP6Hk8jBWFnKYaXg78Wd/rlLI41LxqmXfhyBU4VhepfPS8SfJhLJlqBgyVfZyFk4Exor0RMIJt2BQUPAfPs7NbvhHkcw73PbuXeqe7pFjP5+B0i1or5NH9L/H8oXGk1riWjdQKrY8kEP5l74scrFa56vwze0aELUZTtPseU1KSJJpA7OS5ybdy1ugduHYaUUvlEMs8jx58H2KRJKZAMpR/krHifZwycDue00Bpm1r3PGrB2dSDcxlvXkWSOEzXQwYrPl6G/aoR7RMbI9iGTcNgyedwtZNZMZL3bJ45cJhYrmxautKabzzyEGrBzmLV/3qpFAfrNVrNmPMLZ/NU4bklp7KXKPTPoQSCKCHv+Tx88Gc5WD+f87d9Hd9psr92GU8cfCeRGmSwpPsWRofyj3HFzt/EtgIscWSYsSUkI4VHGC0+QizzRGOD3LPvvxLJAar1gIGSR853+ipIOt2YKQEjFSPaJxpGsA2bhpxnk/edzOktjm1RLvgIVm43vVCsl0IqxcFalYvLFzCQDPBk4RnqTh2F7in9c7TNFfpCbMtioY1PlKSmUTnfZd/0HvZN71l4FKJY9Zg4WaLG6075OK4dkMWseLt2F9uKuHDrH/DggV/Ds8eJQonSp1PwHRbWJ7Y7aQrIiPaJhRFsw6ZisOwTRLLfY0TDtRfv5sEX9vdF2bZlMVIqUu90ieQiNd3LYAHVdotnDh3k1OExboh2EoqIewfvZ9yewMJCo7kkOZ9zkzPx8jaduPc8lFLEUuO7ac5dZtiidsME37UQQqDRjOa/s+giZd85Csm28g940xk/R9E7hEYQyzLPVn+FRPTnx9udGEvAcCW3JkMVDMeOEWzDpsJzLEoFl0ar38lv97ZRrr/kXL710FNHAkoN1150Dm86fzffe/I5bn/0qaM6rgJeqVY5UKvxwIsvcMWuMzl723beVH0D5BOkG1NRJdyZf3KJUji2oNlV5FxrTg+lVFieje/adDIEO5GSKFH4rk0ioegcxrGXdi2cj0BS9l+ai7wdK+SC0V/nofE/wHJ29z2/2Y6xLMFgsb9D1HD8MYJt2FRoDZWCR7sbZ/pl33jFBZy/cztPHRgHDefu3MpAIfUYGS4VcG2bKGu8+SJYQsylTpSemVoAPLD3RbYODFDJFxBdlwr5dJDBzCmFoWR4pEC11iURFvbMv8Q4USilKOQcumGcGe13wgTftZFSMdE+mzjJ4TrZKZG+9weBtaDs0CJmS/5v2df8FYp5ty+abrQibEtQKXivqjWrwQi2YRNiW4KBosd0o79u2XNtxgZKVAr9RlDn7tiG5zxOnMhlMwCWEOwa28LhRp1m0C+WSimeP3yYy04/A42mEQQ8XXmaZ929SCSnyG3ckFxFqeBRb4UUhYttz9irkqZpPMchjPvz8TKRhIlECHhp+iouO/VL2FaEZfVH5FqneWyl0jmVVobToGUpKv6zbE/+hOHiC8R6NxPddxOp7XP7qDUibMuayXcbXi1Mp6NhU1IquLhuxsdbp8Nus3Bsi5/+kTcwWinhWBaubeM5Dlsq5XQQgUiX3wbyeQqex97JCVoZYj1zGCabjZnyP83tA//M4+6zBCIkFgl77f38efQPKD+NXjthmjvXSqNUKviFQvZ5aiBvPcNVp/02N7/ml2gG2zjYuIh5AT4AUllI5VLvbuf5yTfzyIF3E8v+1IbSgkruJXYN38pw/gHG8l/m/OEPUXQfmfcczXQ9IIhX/u3DsPaY26VhUyIQDJR8pqr9zTS+lw7yjTLEZ6Rc5CNvu4Z941WiOKGU83l5eop9E9MoBbu3bOP2Jx4nTJa3Pp1sNrn7mac566IhmnYTJY5EwFpATMwP1KO8uXwFE9UunTChNJOS0DAzed0hTnqj7J0DD3LdOb+PZcVYQlPKHUIpjzuf/X8o+xOcveUOLCth39QeHj3wY4RJBQDXbnP+tm+gdNSTFhFohJBzeX1LJEDCGeXf5PHpv2Z2g1SayVqXrcMF3IwabsP6YwTbsGkp+g5N3+6fUq6hXHCZqmdHi44lGK2UmGq0+Mu7f0gsExKpcCyL58cPr9hzQ2nN/uo0rg5IMuqyFZqXOIjn2OQ8myCSBHbC7HB2raCYd6g15wu2Zs+Zf9yz0GgJsOyIN+/+LLc9/l947OAteHZrpgqkiCViztt6G+ds/Q5SeShl4TnpjcwWksVKQBxRx7f3E8pT5x6TUjNR67J1qLCoHa1h/TCCbdjUDJV8xqP+ZhrPscn5DkGY3Ubueza3P/YkQRTNydlS/tKLIZUiaCdYA1ZPhD1LXucJI8lA2SeY6pDEmiiWFHwbTeqj7TjW3NzJgjdFzmlkHsuyJG+74Ndph1sp59IxZ/XuTqRyGSrsnxN5qRzCpIhtJThOf9flLBpNECmEQ4+mx7Fish4wNpjHaPbxxXyvMWxqfNcmv8hsxNkhuVlorThQrR1z+bEQgq3tLZnHcbTNa5JzSKTCtizyOQfHEXQjSRCrmfOAwrzzl8pHLOHp6lgJg4VXsC2FbSmGCi8zWnqhJyK3rQTfaeIsYyYVJkOM10cz2/2DMGGq3jUOf8eZFQn2Zz/7WW666SZuuukmPvWpT633ORkMa8pgycv8+u44FsVc9pfMtQoctdYcONTgkomLIBHoOP1Bgn6hQLk2BGjCMGGkkqfguyipaHdi4iR9fd51cB2HgjtFwZtisnUWSmef4cL7wmK2s7alZnLVWecMiczx0IFfmZsDGWd8u+gECdVmuHZvlmFZlk2J3HPPPdx1113ceuutCCH48Ic/zLe//W2uv/7643F+BsMx4zkWlZJHdWGZ38z09W4o+wyhcp7LWKXMeD07/bAaDtfrjP+gjrJGEFsisDV6wkVGDvdteZG3XnwhhZzNYNHDEtDsRCitaXaidGKMO80N5/8uQ/mnUMpBCDW3MLnUTMtZFvUKX+TxTryF77/0+4TJCJDm4qv1kOGBfpe/ZjvGtgSDJd/UaB8Hlo2wx8bG+NVf/VU8z8N1Xc466ywOHDhwPM7NYFgTtE7TH15GmZ9lCYqF7Ljl5itfg2vbc2ZLM4PRV43UOvUNkQJ90Efvz0Foo7XmpclJir6D59rEUlIqeHN+1UopWp2QK0/9GCOFJ3CsGM/p4tohQuhMwT0W0Uwja4/79v/nObGeuwalqDbD/pZ/oN6KaGX4txjWnmUF++yzz+bSSy8FYO/evXz961/nmmuuWfcTMxjWEiEEQ5Vcn9MdQMF3cJz+fwo7hwf52evfzEWn7mRLpcIZY6MrC2lXgdKaKJE0WhFBJBFoKvPawAf8Zyi4/397Zx4lV3Xf+c99a+1VvWpBG5sQCBCb5d6GcwAAIABJREFUAQuDjcGGWAZ5wbEcYmsmTgwZIMSxzRAyMSd2fExyPIlnTI7H45MMMQPE9njBxGPM4AUbBNjCgGzEIgHat1Zvtdfb7vzx1K2urlfd1a1utbr7fs4RqF9Vvfe7re7v+73f/S370EZlmUyxGcPs7r+A3YeX4kUIs+cFDBQbJ9NICf2DVZyIUnrF1NJylsi2bdu46aabuOOOO1ixYkXLF+joSE3GLgC6utKT/uxsZT6uGY7fuq2YSaHcmENt2mYYjx1FKm3TnjmPw4Uy//L4Lxo67A2ha2LMIb5RrwjgtEXdJI4ItA8IXae7IwaawPECOrOHmUhuQNFZSMo6MClBD+dHSuy4iRdAMmliGo3zMn0haM/EGybXeFLQmY1jjzHJHtTP+LHQkmA/99xz/Nmf/Rl33XUX69atm9AFenuLkY9R49HVlaanpzDhz81m5uOa4TivW0qKhepwmtwwAtyqSy2imEYGkqdeeg0nokx8iLHEuhm2aXLpqadSLh29UVSrLu0ZG1sXDOZrHJIL4aTWPFfPt0F6BIGBrnvDZemtIiUsyT3LtfE/5rldf8jenstIJyyMUcJcLECl5JBOWA3nKBardI0xhV39jI+Ppommju64t+79+/dzyy238KUvfWnCYq1QnGhoQtCWthuFTEI6ZUWm35m6YOfh3ilPYItZJul4rO6Y7wcMFhw0XZCKW/SVT6avtAIvqPetgkDgB0fT/Tzfxg0SxM0BdD28sUzUyxYi/JOJHeTyU/87SzJPUig7keGRYsWlVHMbgvqVqsdARKdExdQwrmD/8z//M7VajXvuuYf169ezfv16HnrooeNhm0IxLSRsIzI329Q1kvHoh864FZ3LfSwUKlX6iuWG447n05+vkklZGIbG46/+Fbv7LsYPTLzAouZleWbnzTz5+p+yb/BsDuRX8cLeP0ITPoY+NZt/hu7y1pO/hu8FFMoOfkQoqFCKfiIplByK1fFL9xUTR8hmQbkpQoVEWmc+rhlmZt1eEHCgt9zQglUiOTzYGDJ54c3dPPzrLZFTaCYyxWYkGnDdhRexuD0TmSeeTVlYpkFPfyjqhlbB0ssIvRPLtOgvHG08ZRoGv3/+jZh64w1gskgJT2z7C3b2rcU0dDIpsy7UYekDnN75TRZlNiGlRW91HYcqNyAJJ7N3tyewR23mqp/x8TmmkIhCMRcxNI1cqrFznSDs+zyapZ1tTTccJ0sA7O09zO7egchzDxbD+YxDlY5eEKfsdlCuSqSE+IhWp34QcKh0IYGcul9pIeDtp/8D71tzK13JzXWT400tz+UrbmNp9ofY+mFixj4WJr/BadlPAwFBIOkdrEzKWVM0R/USUcxbUnGTctWjMqqfiG3qJOIG5crR49v296BrWmQ/Ef1IMclkeo1s3rEDsWMH7akU699yHgmr/ibSO1ihqy1OzfGGNzYlMFhyyKVtap5P4Id53lsPbqQr+Ty6qKJrUxMaEQKy8QNcveoLBFJjz+Db2Dt4HQvST2HqBfQR/bV1USNhbCdj/pq8ewmuG9CbD3uOKKYG5WEr5jVtGbshPQ0gHbOGhRhCUW62iZewLd52xumkY5MboyWB3mKRHz63peE135cMlhwyo54GpJQUKy7J2NGngbK7kF+8+U/s7F/HYGUpVTeF509N7F2IsJx9We4XvHX5Zzil/fvoWmOcWtcqpK3NR22qegyWatOWNz7fUIKtmNcMla2PRtME6eRRsVt10oLIKkJd0zjzpMWcs2wJ1194Xp3IT5SD+TwHBxvjnJWKB0ISs+tzol3XJ5ABlnn0QbnmdfJyzyf45c6v8t0X7+OX229n/8DZSCmmpHR8KJOkmQAH0sCT9fnGg0WHkqqEnBKUYCvmNeEMyOiy9bhtELNCkUzHY1x7/moMXRuuljR1nY5UkjXLl/Ls9jf49rObG3qSTJSXdu3DHZ0jDuQLDomY2VCpWS57WJaGLuoznwWCZCLGroFLSdh9TUvZpxopNQ6X3zXqGPTlq5MKGSnqUTFsxbxHIGjPxjnUV67fJJOQTlo4bpVASt5y2nJO7u7g+Td3U645LGprZ0VHO798dRtb9+ybEkHa3XeYZ7bpZJMxVi5aQMwMvXw/kFSqHsmESaF0NM9ZArVagB0zGjJNDE3Qke4laR0+ZruaISVIdAJpIJD89sAtHK600ZaRdRklvi/py9fo7lKbkMeCEmyFAoiZGtmIjn6GppFKmOSPiGRnJsW71pwJQM31OTxQ4qU9+47Zsx6iUK3y4q6d6JrGpte2se78NSztaAegUvPIGBZxy6DiHA0xuJ5POmkhtHBKzUgS9mRbVrWGF9jszb+TfPVUDhbfiuPnAJ9i1SM9agJ7perRn68gxLE1qZrPqJCIQsFQaMSqS5UbIhkzsc3Gnhq2qVN0xh4CMFn8IMDzA374/IsMlI5OhSmWXWzbQNePirCuaZi6QNcabay4i3H8zDTZqFFx2nh+783sHvy9I2IdUipHF9UMlpzh4QyKiaMEW6EYQVvGrhPDITIpKzKbpDuXmjLvOgrPD3jwqWd5aNOz9BWLBFJSrjrDk981IcgkLZBhO1atwXbBi/s/hefb+EEo6H6gNUxYnyhSgusneHTr31As+w29VKSU5EtOQ6GRlNA3WEGlZ08OJdgKxQhMXYvsNWJoWiiMo2hLxqelbH0kgZT0Fop891fPIUSAEAJD0+lqi9ORjWEZGoGUBIFEozGFo69yDk+8+U9s63k35VqOoRCJEBBMMnskTPNz6Uy9EfbtrrgNbVc9L6BQaewr4rgBA8Vqw3HF+CjBVihGkYyZJOKNIhy3DGIRI8UWt2ePh1n4gWRn72G6cnHiMZ10MnwaGOnFen6AYTQ+CVS9RRwovhPTqKBr/rCmayKU2cmItqnXWNHxFBCmGFZHT6cHyhWvLt4+RLHsUmoyAFnRHCXYCkUE7Sk7cqhBNm6h6/XH41aj5z0duL7P3r5Bao6P4/iUyw6WZTQ8DfiuRI+wfVluE4bW6PFqAiQT97SlhCA4GjcvV73Izn75ktOQQSMl9KtUvwmjBFuhiEDTBB0RE2o0TZBNWnUpa2eetBBLb9zwm2zec7OPmbrOguzRohQ/kPie3zAwQBIGqLVRN5Yx9VhCxZlYg30vsHn98NHpU1JKSpXG6scgkOSLTkPIZCjVT9E6SrAViibEbb2u2nEI29Lr2rCeuWQhXdkUhl5fym7qE8+abU8mWbfm/IZhtxBuMK5edlLdMccNwkkxowp/fF+GN5sR6r+/cDm+jH4a0DRJ3Gq9i14gBa/3XEbZ6WBB+iVso0DM7OekzM/JWL9GUB8eqbk+xQgxr1Q98mVHla63iMrDViiaIGXY4rTq+NScEQIkIZUwqXkBruujaxob334pjzz3W17ddxAp4ZTuTiqOy67evglds69UIhWP8c7Vq9m07TWqjosE2pIJrjl3Nb4LjGpZUq154fR3X9Zla3iej2Hq+G6ARDJYPYM9g1ezJPs4umjs7zGUH93SJHYkp3f/nJXdP8cLbAy9ihjhQQfSYPOeuzlcvmD4WKniUY2IWw8WHWzLaGjFqmhE9cM+gZiPa4YTf92uH3Cwt9yQuuYFAYcHqni+zzd+/gx7+wZx/VDYdS3cDJzMb9flK89geVcXcdug5jromiAVOzqZJhE3SYzKFzcMDcvUKY/yYjUh0AwNbzgnWnJax0Oc3vkgmog2bjzRblXUpRT8+LV/w5dHezu3tSWwNRpGiFmmxsKORNPRYrMd1Q9boThOWEZYBTkaQ9dIJ01+t2tfnVhDGF+erCu0afs2Xtqzh0rNw5eSp7e9zr/+YhP/59nNvH7wEKWKi+s3ptAFvsQeJeSBlBBIjOHCH8Hh0gUwTt/ssWxvPXwhOaPrgbojrhdQjvCyHTcgX1KhkfFQIRGFYhykhHTCouL4VEZ2nZNhCuCWXXvrxPpY8YOAF3ftZG9fHz2F/HCgIV+p0LPlJdYsz3P5WSvJpeo3P6tO2GskMHXcEVWGnh9gaTqGIfA8yUB1JU6QxBb5SIGcKtEUAlLWzobjxZKLbeoNcfp8ySUeM7F05Uc2Q31nFIoW6cjE6jYWAZBhsc1UE0jJoRFiPYQXBLywcxf5UoVyRMvScsUlPqp0HcBxfSzTQNPgnIVfwdCmv3BFSjhcOrnheCBl2MBq1I0hCGRDLxdFPUqwFYoW0TVBe7Yx1e+yM0/GMhrT+oDGtMApcl/39vVTqfkNec9ShqKdilsNnnKl6rEo8xKLM09gaNMffpBoPL/7/ZG52VXHp1JzGJ1sWK15kdkkihAVElEoJkDC1smkLQZGeIIXnbqUZ17dwWv7enC8MBRh6jpnLVlEb7HInt4BIHQop0IjpQzPj5QUyy65UfF1zw9wXJ9UwqZQqo34nKQrHmaITCdSghfE+Nmrn+KcRd/jlM4nEZpg7+CVHHT+kIy9g9UL/gdt8ZeRGPTX3s6e4m34MqwYHSjWiNmNIROFEmyFYkJICdmEFVYaHglJaJrGreuu4Lc79/HUyztAwpoVSzB1jX/9+TNHPwv4U5SUVXVdyrUaCWwqjkd8VPFMpebRZukk4mZd5ojEa9mzbjUbZOi9YV8Sg+0972DL3g9wzVmfJ2X3DI8SO6X9e5zkP4ml92Jo4U1D4NJm/5yk8Spb+/8XYOD7kv6CQ1c2NsYV5yct38KKxSLvfe972bNnz3Tao1DMCtozsbrSdU0I1qw4iZuvvYwPXXYBpyzo5JnX3sTzp6H0WkqeePk17vvFJp7d/gblSnRJ+EDBIZWwMEfYuS9/BZ7fKITN7iOtZuQKwXCa4Kldv+SD599Kyj5UN/dR11xixkE0UV8erwkPUztM1np6+Fil6kZmk8x3WhLsF198kY985CPs2LFjms1RKGYHuiboyMYaWq5qAtrSNpoQDJQrY5eDT5KAsK+IHwT8ZsdO3jjUQ7naGPeVSAYKVdozseFpND2lC+ktr8ELjoq2F1hU3U78wMIPjCP/N3l+9wZcP9FyeqIQYOgupl5F1/zIye2a8CPzv3WtQsJ45ajtEvoLtYb2rPOdlkIi3/rWt7j77ru54447ptsehWLWELd0ckem1IyUFUMLB/uu6Opgf39+2vtlv7BjFyd3dVIz/YZBC47jU/N82rIxegcqSKmxee9fsTC9ieVtP8XQJDv73sHe/OUkrP10p36FlAYHCmvpLWbZ0XsZl5z8P1mc/e2ENymjQirNwix+YOMG3fVr8wIGSw7taVtNqDlCS4L9hS98YbrtUChmHfLIzMeaGzQ0PYrbBletWcnm13dNq2ADlGphiKFc87AMDTFKEfMFhwXtcbJJm4FiDdA5ULicA4XL6cjGjnixDiVnCW/2LRn+XDIGpepSnnnzJj5w3q0TtitKmANpIiUYWv33S6LRV3tnw/uLpTBNMRYx8Wc+Mu2bjs1KLFuhq2ti3cPmAvNxzTC7153LJdh/uIQzatp5Jh3jP9/wLv7r935CsTo9mRkCOHlBJ/Fk2GBEmAapiF7erhQsXpDGSpiUK0dDFYHQ6OyME0+6FEpOQwgnlbJxa0kCqaOLiRUHhQN6NQKpI/ARQtJbXk3JX8Oy9L8hMQBJIC1e6vscwmojFzEkQmoa7e3Jhra2s42p+BmfdsFWvURaZz6uGebGug0kvYOVhn4ji7IpPvjW83ngiV+N2fvZNgzOWLSQLbsntqkvgTMXLaRyJH2vVnHxU1bDBPUi4LkeqbjJYNWj5o4Y4uu4pBMW0vcplqNyoLvwAxtdK0/INiFABgFSmggh0YRHR+Il2nmZ3+z7DIG08AOb/sqZgI6uFfBycSImsRG4YYOr2YrqJaJQnECYukZbNtYQBtA0wcUrl3DRacsbRHQkXuDTVyxO+LqagL19YZ63lJJt+w/yv594ln/56SZ+tW0HrnfUKy6UXFw3oDMbq8scKVU8XD8gnbBIxKN8OIE2jnfdLMYsBBhabXgDUtdcDK3GmkVfprd0Hv2Vs4GhWZMBpVp00cxAsXE+5HxECbZCMUWkYgaZiCZRpq7zB2+/kD+95u10Z6M9Jz+QHC6WIl8bi0DC7r4+pJQ8/rutPPbb3/HGocPs7OnjsRdf5uuPP4njeUeuETBYCQcJdGbjw+XrUoYDBjgyOT5mjY4XB+ha85CO7zd/UBeNIybD4/jk4q80HC9X3IanFAg3IFUF5AQF+6c//SlLliwZ/40KxTxESsgmLeIRcx9jls5piztYtXhhU087ZduRx8dj9+E+Ht78PK/sO1CX9+36Pr2FEptf3zV8rFr1qLp++NidjQ+nJTquT6nmIhBkUzGsuk0+jZJTPzhhiEBqPLvj47x28KoJZXLoWg0hGtP+gkCGKYoR36J8yYkU8/mE8rAViilEEI4WM83GJlEJ2+BtZ53SkMUBYUjlslWnTeqaju+zu68/8jUvCNiyoz4uXiy7BFJi6RrtmaNhnGLJxQuCMJc8ZWOOEO2Xez6OF9TfUDzfYnvPO9jW8y6e3fEJal7rCQaCgIRxIPK1cs3D9xuF2fclhXk+nUYJtkIxxeiaoDMXj/SkVyxoY8PbLsTUdWzTwDYMDF3j3WvO4uzli5o2kToWRqcVOq5PtebhB5KYqZNLh6I9souepgnaR4j2oeIlPL/3Tgq1pUgpqHkZXjv8YX61808BkOg8se3TuH5rOdNCwPK2RyJfCwIZOWkdoFB2cdz5O7hX9RJRKKYBS9doz8boHag2bJa97axTOG1RNzt7+ymXamFanmWydc/+abFlWWf78N+llLyy9wC/2r4Tx3M5d8VJvPv8M0gnbfLF2pEuemFvEk0TtKVs+opVPDfgUOliDr15cd25M6mwAZXr+hzIn833XvgKHzjvP2Ho45eVm3rzrJNyxSMZMxom0ASBZKA0f/uMKMFWKKaJZMzAT1v0F2p1XqcmoDuXoC2TYGCwMnz8QH9+uNvfVHLRacuH//6j51/iN2/sHh64cGCgwJNb3+Bv/uAaUgmTYtmlUHKxDB1dE2FL2VRsWLRHowtBJmlSrgoqVZ+K2862Q1exauGPxwxdBBIOFS9q+rofBFQdv6GpFYRx+FoymJczIOffihWK48TQpJp0RDGIoWm0Zep7a+eS8bBt6hSypL2N7mwGgN5Ckede31U3HcfzA0q1Gg8/+xJtqRhx28APgrqNvyHRNpoIpECQjJlkUha6oTFeE1kpwfWTbO/90JjvK1aiNx8DKRks1KamV+0sQwm2QjHN5FJNMkfsMA1w6LF/9dLFY+Zqj0QDLGPsntFLO9p57/lrcI9kjmw/0BP5Pj+QPLd9F54f0JENM0RKVQ9vROWmromGDoWjsQxY0fkmp3f/dEzvuuy08cOt/4Djd425Rs8L+3pHUXW8+nFt8wQl2ArFNCMQdGZjWKMzRwh7jgzlbtumwX+8ci22OX6kUmiCGy+7lMtXreT85UtZuWgBSdsONzzTKa6/8Dzed9H5mIZOtRaKnqHpkRkqAIWqw9999yeUqg6duTiGLiiMynvWhaA9HS3aGXs7V536H7h06X9B15yG14fwA4PNuzbiBQvGXSOEGSNRnrSUMBgxZmyuo2LYCsVxQBOCrlycg32V+h7ZEhIxYzhDY2Fbhs9c/y7u/8Wz7Ontj8w71oTglO5uUrEYZy+Nzo8eiecHeIFk1ZKF/N/f/K7p+14/cJj/9oMnuPOGq+nMxekZqFDzfOwRmSu6For2YLFG7Yj3q4sKly67C1Mfu/BHSugrr+JQ6XISdmvS4zgByCoCkNRvNIbZLn5Eoc/cRXnYCsVxwtA1OnKNPbSRkIqZpBJhrwzT0Pmjd67l5ndfwXvOX01XJoWpa8MhkMVtOd65elXrF5YSzwtI2hbXXXTOmG/d2dPPrp5+BNCVi1OpNYYkdE3QlrGJHRHdRZknEeOUrgdS40DhrWwd/AcSsVhTT38kCXM/F510B+d3ruO8znWszN1CTH9z5LLIl5t783MR5WErFMeRmKnTnrHpHWycWp5OWEjJcKvW7mya7myaS1aezMGBPL3FEnErRtqaeEpb1Qk90TUrlvDwr7c07cshBOzvz7O0sw0hwvi74/lYozZDBYJcyqKgCWJGD7qInsIeSI189WTe6LuB/YXLSaV1YPwSc0MrcNnyT2LoRcSRgQdJYysrc7eyte8beLIDgFrNp+bNn4wRJdgKxXEmFTejR4cd6eURSNmwobYgl2FBLsz2KFXdCW24FSpVNr+5gz19fcQti+5smgMD+cj3CqA7E1YsShmGX+K2iQwCRjcbFAgyCQuHVXhBHFOv1L0eBBr7C5fzwv6JDz5Zkv1/aJpTN51GCImGQ1f8++wvfzy8xpFQUiwXmxdDDpRgKxTHGSkhm7LxEAxEvJ5NWshAUnWiwwzJmImua5TKLlJKpJS8tGcvz725k3LNoSOdYu3pp7Kko518pcK/bfoVju8hJQyUKhiahiZEpJe9oC3D8u6jhTaBlGg+JBNW08ZMrliLG3ShiX11Y8ECTLb3bpj4Nwhoi786PKh3JJpwSZpb645Va2G3wfkwZX3ur1ChOBGR0JlLEI/YfBMIcmm7YdzXSGKmTjZtYxg6m17bzi9f2Ua+UsULAg4O5nnkNy+ys6eXZ7a9geN5dd6nFwQgJUs7cghCL1oXgpO7O7j1PVc0xJcDKanUXNqysei0Q6mzLX8vfdUrCAIDKQUDldN5ZtcXKTrLJvXtKTkn4QeN/a+l1Kn69Q3o/EAOT7Cf6ygPW6GYIUwj3IQ81Fdu6I8xJNp9hRpuk1xkQxOYpuTFXXsa+oV4QcAvXnmNmutGDgLWdY01K5ay8R1vpbdQIhGzyMRj6JrOkZSM+vN5Esf16GqL09PfOKjBDzLsLn2WN/MeA6UKrntsvuCugd/j5PaHGR3vDjDoqXyg4f2Fsks6YTaUss81lIetUMwguhBH8p4bfxU1Ud+AKYoD/fnIzwIMlMvUvGjPUwiBbeiYhs7CtgyZeLiRWalGd8oDKJY9NL15YysAQzfoyKSbDEJonarXxeY9n6XmZXH9OJ6fwAvSvJm/m5q/vOH9nhdQaRJCmksoD1uhmGFMXaO7Pc7BvnKDWGqaoD1tM1A4mvc8kqRtjzmCr1k2iJRwxkkLI99fcTxSEeO4gkAykK/RlYvTkYtzeKASeW0BZBM2pq5TKE1+UkxveQ2Pb7+fbOx1DB2s+Dkgm0tWoeSSiOg9MpdQHrZCcQJg6hpdbYlIz1UTglw6hh1RILIglyabiE8oEGDqOr+/9oKmFZXlqodsIrKVmnekKZNO1xieNoT9vztysTGfEMZHZ7C6koHKKqQc+zyO6485N3MuoARboThBsA2Nzly8sbCGsMNfW9puqOoTQnDjFW8hm4hjGTqWHnbZa1aYIoBbrn07Kxc3Lw33/QAnKu2QI8UqpXCIQMzS6e5IjNlfxNA0OjI2qbjZUrHMmIzjqAeBpDbHe2XP7ecHhWKWEbN0Opr00R7aiBwoOlRrR2PT7akkt7/3new81MtguYpt6nznmRfquvINoWmCdHz8UWSVmhdmqUSIZNXxqDg+MVPH0jUWtIcbkc0GCwgE6aRFLGaA0Jj4qGHQdYHQxLiiXa64pGLGnM3JVoKtUJxgJGMGMhtWQ44WnqEKw0FBXfGMJgQnL+gEwiEFmUSMvkKpTt90TbDqpIUYLbRwdZwAKWVk1sWQlx3LxYHQi17QnuDwYLV5QY8EU9PIZuP4rkeh4tZ1AxwPy9TGFWuAmuvjB7Kube1cQoVEFIoTDCnDasi2tN1k4rggl7SbZmIIIfiDt72FhG0NDyKwDJ2OdIr3Xjh2L5Eh/CAYM7xQrXnURghu2NwqRjLRuFlZZ5smiFkGndlY2D+7hWKXsNqyNd/S9+d2WER52ArFCcjQ8IOwWb8T6VxmEzYaImz0P4rOTIq/uO5qXtt3kIFyhQXZNCcv6BzX83Q8nxd37OHlvftJ2hZXrVnJmUsa491SQr5Yo7stMbxBKRB0ZmIYmiBfcsYMSwgESdskYRs4bkDF8XCcoCGfXNc0MklzQlWM5apLwtbnZFikJcF+5JFH+OpXv4rneWzcuJEbb7xxuu1SKBRANhkOtR0sRnelSycsNF1QKLrIUbJu6BpnLV3U8rVqrsfXH38yLHw5Ev9+Ze9B3nH2adyw9ryG91drPjXPxxqVB55LhX25Bwrjp/QJBLapY1s6QSDDzc6hVEERDmmYaHijWvMJmoRzZjvj3rYOHjzIP/7jP/Lggw/y/e9/n29+85ts3779eNimUCgIBTCdbB5qSMZMcmnrmOO2T7/6Bv3Fct1mpeP5/Oy32znQ39gsaqjxUtRlM0mL9qhWss040mgqZujELCP8YxqTWpMfBDjeHHSvaUGwN23axKWXXkoulyORSHDNNdfw6KOPHg/bFArFEdrSNol4E9GWELMM2nNjj/Aajy279kbmMQcy4IUdeyM/U6l6wyPI6kySkLQNutvHTvubDqQMUxPnIuN+Jw8dOkRX19HZa93d3Rw8eHBajVIoFPWEY8bsMTf1TE2jvUmBTSs082YFoulrfiApjdF4yTY0FrYnImdaTidRN5G5wLjfxSAI6hLepZQTSoDv6EhNzjKgqys96c/OVubjmkGtu1U62gMO9VcoVZsPAWjLxRko1sYU0iguPmMFj/3m5Yb8baEJ3n7e6eTaEpGf0zRBri2BaTS/UXR1pekbrJAvOU3PM5UkYgZdnZPXnulgKn7GxxXshQsXsnnz5uGve3p66O7ubvkCvb3FMXsdNKOrK01PT2HCn5vNzMc1g1r3RDGAwPXIN9mIhPDR2UCSLzkt//6dv2wpz2/fTU++iOv7CBEO7v29C87ERmegv9z8er5PMqL/yEiECMeOvbGrP3qAwxRSsXQsaFpif7yZyL+1pommju64IZG1a9fy9NNP09fXR6VS4bHHHuOKK66YmLUKhWJKaUvbZFPWmHkQccugIxtreUitaej88dWX8f5L1nABzMmnAAAG2klEQVTOssVcdOpyPn7VWq694KxxP1uouJGbjyOREjIpm4Ud0x8i8QPZkDUzFxj3u7ZgwQI++clP8rGPfQzXdbnhhhs499xzj4dtCoWiGTLMHhEiTPlr5kgamkZbJkal5rXkbeuaxuqli1m9dDFAy+FP1w1wvACzSavX+msIunNx8mWHwWLrTwATJaKt96ynpdvcddddx3XXXTfdtigUigmSTdogBIOFWvNCERl626ahUSg5TUePRaEJQSuZeUEgqdY8zITV8rmzSQvbMujLV3CcqQ2RiOH/zi3JVqXpCsUsJ5uwmpaxj2TI286l7ZZT7QxDtJxLXay4TKRWRcqjWSSduVjTQQyTQZ/Cc51IqNJ0hWIOkElaCCHoz9fGri484m3HTJ2q61McowmTEIJUwmrZSfU8iesGmBPMuxYIkjGTmGVQKDsUyu4xh0nitn7CbDhOJUqwFYo5QNh7xEQI6BscR7QJxThuGcQtg5rnU3PCP1KCRKLpgnTMxDJa65IHYeVj2fHIGq2HRUaia4K2tE0yZjJQrFGpeZPqB6IJgT1HJ89M+6paLk2d4s/OVubjmkGte6rIJC0MQ2egUGvZS7VMnXQcECCDMLdCa6H3dBSuF4y7pvFety2dBe0Jqm5AvlTD84IJCXcybpCwjRPOw27133qs9wl5oq1KoVAoFJHMzci8QqFQzEGUYCsUCsUsQQm2QqFQzBKUYCsUCsUsQQm2QqFQzBKUYCsUCsUsQQm2QqFQzBKUYCsUCsUsQQm2QqFQzBJOWMHes2cPN954I+vXr+ejH/0oe/dGDwGdaxw6dIhPfOITvO9972PDhg3s2bNnpk06bmzdupWzzz57ps04bjz33HPccMMNrF+/no0bN875n/FHHnmE97znPbz73e/mgQcemGlzjgv33nsv69atY926dfz93//9sZ9QnqB8+tOflg888ICUUspvfOMb8lOf+tQMW3R82Lhxo3zwwQellFI++OCD8vbbb59hi44P5XJZbtiwQa5cuXKmTTluXHnllfLll1+WUkr57W9/W958880zbNH0ceDAAXnllVfK/v5+WSqV5HXXXSe3bds202ZNK0899ZT88Ic/LGu1mnQcR37sYx+Tjz322DGd84T1sIMgoFgsAlCpVIjFYjNs0fTT19fHK6+8woYNGwD44Ac/yJ//+Z/PsFXHh3vuuYeNGzfOtBnHDcdxuP3221m1ahUAZ5xxBvv3759hq6aPTZs2cemll5LL5UgkElxzzTU8+uijM23WtNLV1cWdd96JZVmYpsmpp57Kvn37jumcJ2wPwttvv50NGzZw//3347ou3/zmN2fapGln9+7dLF68mHvuuYfNmzfT1dXFX//1X8+0WdPOT37yE6rVKtdee+1Mm3LcsCyL9evXA6Fzcu+993L11VfPsFXTx6FDh+jq6hr+uru7my1btsygRdPP6aefPvz3HTt28KMf/YiHHnromM4544L9ox/9iC9+8Yt1x0455RRqtRqf+9znuPrqq/nxj3/Mrbfeyg9+8IOWZ8yd6ESte/ny5WzdupXbbruNv/zLv+Tb3/42d955J/fff/8MWTm1NPu3LhaL3HfffTNj1HGg2brvu+8+HMfhzjvvxPM8brrpphmycPoJgqDud1dKOWd+l8dj27Zt3HTTTdxxxx2sWLHi2E42NdGaqaW3t1defPHFdccuueQS2dvbO0MWHR927twpL7jgguGvy+WyPPfcc2fQounnW9/6lrzqqqvk9ddfL6+//nq5cuVKef3118tCoTDTpk07xWJRfvSjH5W33XabrNVqM23OtPLd735X3nXXXcNf33vvvfIrX/nKDFp0fNi8ebNcu3at/Pd///cpOd8JGcNua2vDtm02b94MhLvpyWSS9vb2GbZselm2bBkLFy7kiSeeAOBnP/sZq1evnmGrppcPfehDPP744zz88MM8/PDDADz88MOkUqkZtmz6+cxnPsPy5cv58pe/jGVNbkrLbGHt2rU8/fTT9PX1UalUeOyxx7jiiitm2qxpZf/+/dxyyy186UtfYt26dVNyzhN2gMGWLVv4/Oc/T7VaJZlM8tnPfpazzjprps2adt544w3uvvtu+vv7SaVS3HPPPcf+GDWLOOOMM3j11Vdn2oxpZ+vWrbz//e/ntNNOwzDCyGR3dzdf//rXZ9iy6eORRx7ha1/7Gq7rcsMNN/Anf/InM23StPK3f/u3fOc732HZsmXDxzZs2MBHPvKRSZ/zhBVshUKhUNRzQoZEFAqFQtGIEmyFQqGYJSjBVigUilmCEmyFQqGYJSjBVigUilmCEmyFQqGYJSjBVigUilmCEmyFQqGYJfx/CVeXf7IwtGMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from matplotlib.patches import Ellipse\n",
    "\n",
    "def draw_ellipse(position, covariance, ax=None, **kwargs):\n",
    "    \"\"\"用给定的位置和协方差画一个椭圆\"\"\"\n",
    "    ax = ax or plt.gca()\n",
    "\n",
    "    #将协方差转换为主轴\n",
    "    if covariance.shape == (2, 2):\n",
    "        U, s, Vt = np.linalg.svd(covariance)\n",
    "        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))\n",
    "        width, height = 2 * np.sqrt(s)\n",
    "    else:\n",
    "        angle = 0\n",
    "        width, height = 2 * np.sqrt(covariance)\n",
    "\n",
    "    #画出椭圆\n",
    "    for nsig in range(1, 5):\n",
    "        ax.add_patch(Ellipse(position, nsig * width, nsig * height,\n",
    "                             angle, **kwargs))\n",
    "\n",
    "def plot_gmm(gmm, X, label=True, ax=None):\n",
    "    ax = ax or plt.gca()\n",
    "    \n",
    "    labels = gmm.fit(X).predict(X)\n",
    "    if label:\n",
    "        ax.scatter(X[:, 0], X[:, 1], c=labels, s=40, cmap='viridis', zorder=2)\n",
    "    else:\n",
    "        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2)\n",
    "    ax.axis('equal')\n",
    "    \n",
    "    w_factor = 0.2 / gmm.weights_.max()\n",
    "    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):\n",
    "        draw_ellipse(pos, covar, alpha=w * w_factor)\n",
    "\n",
    "\n",
    "#用椭圆形来拟合数据\n",
    "rng = np.random.RandomState(13)\n",
    "X_stretched = np.dot(X, rng.randn(2, 2))\n",
    "gmm = GaussianMixture(n_components=4, covariance_type='full', random_state=42)\n",
    "plot_gmm(gmm, X_stretched)"
   ]
  }
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